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SCIENCE ASIA
Volume 47, No. 01, Month FEBRUARY, Year 2021, Pages 106 - 110
On the divisibility fkfx2 + fx + 1
Florian Luca, Prapanpong Pongsriiamb, Laszlo Szalay
Abstract
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Let F n and Ln be the nth Fibonacci and Lucas numbers, respectively. We show that if Fk j Fx2 + Fx +1, then k 2 f4,7g; if Lk j Fx2 + Fx + 1, then k 2 f2, 4g.
Keywords
Fibonacci number, Lucas number, divisibility, Diophantine equation, factorization
SCIENCE ASIA
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